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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.12785 |
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| _version_ | 1866909886467538944 |
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| author | Liessi, Davide Santi, Enrico Vermiglio, Rossana Thakur, Mayank Meijer, Hil G. E. Scarabel, Francesca |
| author_facet | Liessi, Davide Santi, Enrico Vermiglio, Rossana Thakur, Mayank Meijer, Hil G. E. Scarabel, Francesca |
| contents | MatCont is a powerful toolbox for numerical bifurcation analysis focussing on smooth ODEs. A user can study equilibria, periodic and connecting orbits, and their stability and bifurcations. Here, we report on additional features in version 7p6. The first is a delay equation importer enabling MatCont users to study a much larger class of models, namely delay equations with finite delay (including delay differential and renewal equations). This importer translates the delay equation into a system of ODEs using a pseudospectral approximation with an order specified by the user. We also implemented Lyapunov exponent computations, event functions for Poincaré maps, and enhanced homoclinic continuation. We demonstrate these features with test cases, such as the Mackey-Glass equation and a renewal equation, and provide additional examples in online tutorials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12785 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New functionalities in MatCont: delay equations and Lyapunov exponents Liessi, Davide Santi, Enrico Vermiglio, Rossana Thakur, Mayank Meijer, Hil G. E. Scarabel, Francesca Dynamical Systems MatCont is a powerful toolbox for numerical bifurcation analysis focussing on smooth ODEs. A user can study equilibria, periodic and connecting orbits, and their stability and bifurcations. Here, we report on additional features in version 7p6. The first is a delay equation importer enabling MatCont users to study a much larger class of models, namely delay equations with finite delay (including delay differential and renewal equations). This importer translates the delay equation into a system of ODEs using a pseudospectral approximation with an order specified by the user. We also implemented Lyapunov exponent computations, event functions for Poincaré maps, and enhanced homoclinic continuation. We demonstrate these features with test cases, such as the Mackey-Glass equation and a renewal equation, and provide additional examples in online tutorials. |
| title | New functionalities in MatCont: delay equations and Lyapunov exponents |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.12785 |